Red-Eye

When you take pictures of pirates and they're ready for the heat of
battle, often times their eyes would fiercely glow with the red fires of
damnation itself! (Because pirates hate having their picture taken when
they haven't had time to properly primp.)

But red-eye isn't a problem only associated with pirates; it can happen
to anyone in situations where the flash is fired in a dark area.

Basically what happens is that the light from the flash goes directly
into your eye and reflects off your retina (the back the of eye) which
is nice and red. This reflected light is focused by the lens in your
eye and is directed right back at the camera like a fricking laser beam.
Pow!

What can you do to prevent this? Many things:

Get more light in the room to cause your pupils to narrow. This
allows less light from the flash into your eye and minimizes the
effect.

A variant of the previous item exists as a built-in feature on most
cameras: anti red-eye mode. Make sure it's turned on. This fires a
pre-flash before the exposure is made that causes your pupils to close
before the main flash goes off.

Don't point the flash directly into the eyes of your subjects. Not
only does it increase red-eye, but it makes them see those spots that
everyone hates. Of course, if you flash is fixed to your camera, it is
tough to change the aim. In general, the farther offset the flash is
from the camera lens, the better the results will be. Also, if your
flash allows it, you might try angling the flash upwards to bounce it
off the ceiling.

Have the subject /not/ look directly at the camera so that the
fricking red laser beams don't go right back into the camera lens. Have
the subject look at something near the camera instead.

Don't use the flash... try increasing your ISO, increasing the
exposure length, or widening the aperture to get a good exposure
without a flash.

Post-process the final image. Photoshop and a lot of other types of
software have a red-eye removal tool to get the red out. This is not
cheating, provided you draw a goofy moustache on the subject at the same
time.

I don't like the flash very much, and tend to avoid use of it like
the plague. (Perhaps not quite as much as I avoid the plague, to be
honest.) Whenever possible, I open the aperture (lower f-number), or
increase the ISO to get a good exposure.